Data transmission or recording using a frequency-modulated carrier is accomplished by deviating the carrier frequency in response to the amplitude of a data signal, and by transmitting or recording this modulated carrier frequency. In a typical FM system, the magnitude and polarity of the data signal determine, respectively, the amount and direction of the frequency deviation of the carrier. A "dc" (non-time-varying) signal, depending on its polarity, either increases or decreases the carrier frequency, while an "ac" (time varying) signal alternately increases and decreases the carrier above and below its "center", or unmodulated, frequency at a rate equal to that of the data frequency. In the typical ("linear") FM system, where
F.sub.C = THE UNMODULATED CARRIER FREQUENCY, AND
F.sub.D = the carrier frequency modulated by the data,
The amplitude of the data signal is expressed by the relative frequency deviation of the carrier. The instantaneous value of the data, A.sub.D, is given by EQU A.sub. D = [K(f.sub. D - f.sub.c)]/f.sub.c, (1) EQU K= a constant
where the ratio K/f.sub.c is the scaling factor for the channel, i.e., in a system where K/f.sub. c = +0.01 Volt/Hz, a positive 100 Hz deviation of the carrier would be equivalent to a data signal of +1 volt. EQU (+0.01 V/Hz.times. (f.sub. c + 100- f.sub.c) Hz= +1.0 Volt)
Because the data information is imparted to the carrier by deviating the carrier frequency, the demodulation (data recovery) process must determine, from whatever deviations are present in the carrier, the original form of the data signal. Any external factors which are capable of altering the transmitted and/or received frequencies, hence, will be demodulated and exist as undesirable, erroneous "noise" components in the demodulated data signal. If these noise-inducing factors are not precisely known, then the exact value of the original data signal can never be determined.
For this reason, many FM systems employ a reference frequency, a known frequency which is transmitted or recorded simultaneously with the data-modulated carrier frequency. It may be assumed that whatever system perturbations have caused variations in this reference frequency from its known value will also have caused instantaneous related variations in the data-carrier frequency. By accurately knowing how the reference frequency has been affected, one can theoretically, with sufficient knowledge of how these known influences on the reference signal would have affected the data-modulated carrier, in effect go "backwards" and reconstruct the true value of the original data signal. Let
f.sub. R= the transmitted reference frequency
f.sub. D= the transmitted carrier frequency modulated by the data signal
f.sub.R ' = the received reference frequency (system perturbations have changed f.sub.R so that f.sub.R ' no longer equals f.sub.R)
f.sub.D ' = the received data-modulated carrier frequency (the same perturbations have also changed f.sub.D in the transmission process so that f.sub.D ' .noteq. f.sub.D)
Let EQU E.sub. R = (f.sub.R ' - f.sub.R)/f.sub.R, (2)
the known transmission error experienced by the reference channel, and let EQU E.sub.D = (f.sub.D ' - f.sub.D)/f.sub.D, (3)
the (unknown) transmission error experienced by the data channel
With sufficient knowledge of the overall system, one can define a term S which expresses the instantaneous relationship between the transmission error in the data channel, E.sub.D, to the error in the reference channel, E.sub.R, i.e., let EQU S= E.sub.D /E.sub.R ( 4)
if one knows both S and E.sub.R, E.sub.D can now be found by EQU E.sub. D = S.times. E.sub.R ( 5)
replacing the now known value for E.sub.D into equation (3) results in EQU f.sub. D = f.sub.D '/(1+ E.sub.D) (6)
which equals the frequency of the data carrier with the transmission error removed.
The true frequency deviation and, hence, the true value of the original data signal can now be found by demodulating f.sub.D.
The overall expression for the amplitude of the data, A.sub.D, as a function of the received data and reference frequencies and the system function S can be found by combining the expressions for S and E.sub.R with equation (1) or ##EQU1##
In any real FM data-transmission system, it is never possible to determine exactly the value of the original data signal. Digital systems are limited in accuracy by non-infinite word length which results in quantizing error, the uncertainty resulting from the finite size of the smallest incremental change which the system can express. Analog systems are limited by residual noise which generates output signals even when no input signal is present. Because the presence of noise limits the accuracy of an information system, it has become common practice to express the accuracy of a system as a ratio of the maximum amplitude of a transmitted signal to the amplitude of the system noise. The signal to noise ratio, or S/N, is usually expressed in decibels, or db. ##EQU2##
Thus a S/N of 40 db would indicate a 100:1 ratio, or a system uncertainty of one percent of the value of a maximum amplitude signal. When the noise is not uniform, but varies with the amplitude of the recorded signal, then a S/N figure would include this "gain" noise or "percent of signal amplitude" noise as a separate, specified term. Because of the often complex waveforms associated with noise signals, care must be taken in interpreting S/N figures regarding the units of noise measurement, bandwidths involved, and other related variables.
The frequency modulation technique is usually selected for its ability to transmit "dc" information, and for such a system's relative insensitivity to amplitude variations in the transmitted and received carrier waveforms. But because the information is contained in the frequency rather than the amplitude of the modulated carrier, an FM system is extremely sensitive to unwanted frequency variations. In a magnetic tape recording/playback system, flutter (unwanted variations in tape speed) is unavoidable, both during recording and playback. These velocity variations in the tape speed frequency modulate the already modulated carrier. The effect of flutter on the FM carrier is instantaneous multiplication of the recorded frequency by the instantaneous value of the cumulative record/playback tape velocity, which equals (1+ F) where F is the cumulative instantaneous record/playback flutter, or velocity error. Thus F becomes a mathematical factor common to all signals simultaneously exposed to the speed variation. A +1 percent flutter (i.e., F= +0.01) would cause a 3 KHz carrier to appear as 3030 Hz, a 5 KHz carrier as 5050 Hz, etc. [Errors such as these in the time-base (absolute frequency) accuracy of the data can be eliminated only through use of a buffer system, where data is input at a rate modulated by the system flutter, but output at a corrected rate determined by the original sampling rate or some other reference rate. Fortunately, these flutter-generated time-base errors are usually insignificant compared to the corresponding flutter-generated amplitude errors in an FM recording system (as evident in FIGS. 10, 11, 12). All references to "noise" will refer, as is customary, to amplitude error rather than to time-base error, unless otherwise indicated.]
If one lets
F= the cumulative (for both recording and playback) instantaneous flutter, or speed error, in the velocity of the magnetic tape,
f.sub. c = the frequency of the unmodulated data carrier,
m= the amount of modulation of the carrier due to the data signal, i.e., m= .+-.0.5 for .+-.50 percent modulation),
then in a typical ("linear") FM system EQU f.sub. D = f.sub.c (1 + m) (8)
which equals the frequency of the recorded, data-modulated carrier, and EQU f.sub.D ' = f.sub.c (1 + m) (1 + F) (9)
which equals the instantaneous frequency of the same signal, f.sub.c (1 + m), upon playback, with an instantaneous cumulative flutter of value F.
If the reference carrier, which by definition has a known modulation (usually zero), has been recorded simultaneously with the data carrier, then if
f.sub.R = the frequency of the recorded reference carrier, then EQU f.sub.R ' = f.sub.R (1 + F) (10)
which equals the instantaneous frequency of the reference carrier, f.sub.R, upon playback, with an instantaneous cumulative flutter equal to F.
Equation (9) demonstrates the non-uniform effect of the flutter, in that the frequency error caused by the flutter is multiplied by (1 + m), or by the data modulation itself. Thus a one percent flutter will cause a one percent change in the carrier only when m= 0, or when no data is present. In a system where the modulation is symmetrical about the carrier frequency, the absolute value of m must be less than one to prevent the carrier frequency from going to zero at m= -1, so that the effect of the flutter is nearly doubled as m approaches +1, and approaches 0 as m approaches -1.
In the most widely used method for reducing flutter noise in FM recordings, a reference carrier with no modulation is recorded simultaneously with the data-modulated carrier, either on the same channel (or track), or on a separate channel. Each channel is demodulated via a limiter (to lessen the effects of amplitude modulation), an FM discriminator such as a phase-locked loop, or the more common constant-energy pulse generator (a monostable multivibrator), and a low-pass filter. The output of the reference channel is then substrated from the output of the data channel. As previously stated, in a typical FM system the output signal or voltage is linearly proportional to the deviation of the carrier, i.e., EQU V.sub.out = K[ (f.sub.D - f.sub.c)/f.sub.c ]
Substituting the expression for the played-back frequency of the data channel (equation 9) for f.sub.D in the above equation, and letting K= 1 for the sake of simplicity, yields ##EQU3##
Substituting in like manner the expression for the reference channel playback frequency (equation 10) results in ##EQU4##
Subtracting the output of the reference channel from that of the data channel indicates that ##EQU5## or that the output signal consists of the desired data term, m, and a data-modulated flutter-generated term, mF.
It is immediately apparent that this flutter correction method is far from perfect, in that a noise term is present except when m= 0, i.e., the effect of the flutter is only removed when there is no data being recorded.
Equation 11 shows that without a reference channel, the ratio of noise to maximum signal output for the data channel would be EQU N/S.sub.max [Data Channel] = [ F(1+ m)]/m.sub.max ( 14)
Because practical considerations limit the allowable modulation to less than 100 percent (i.e., m.sub.max must be less than 1), equation 14 expresses the "flutter multiplication" effect on S/N, in that a certain percentage of flutter will result in a greater percentage of noise relative to the maximum possible signal.
For a modulation equivalent to .+-.Full Scale of .+-.50 percent, the corresponding N/S.sub.max figures would be
______________________________________ m N/S.sub.max ______________________________________ "Positive Full Scale" +.5 F(1.5/.5) = 3F "Baseline" 0 F(1/.5) = 2F "Negative Full Scale" -.5 F(.5/.5) = 1F ______________________________________
i.e., the effect of the flutter is doubled at m= 0, tripled at +Full Scale, and in a one-to-one ratio at -Full Scale.
Because subtracting the output of the reference channel results in an output by m + mF, the noise to signal ratio is improved, and expressed by EQU N/S.sub.max [Data Channel- Ref. Channel]= mF/m.sub.max ( 15)
The corresponding N/S figures for the same .+-.50 percent modulation are
______________________________________ m N/S.sub.max ______________________________________ +.5 F 0 0 -.5 -F ______________________________________
It is apparent that this technique for flutter compensation is only effective for small amplitude signals (m near 0), and that the effect of the flutter is still 100 percent for signals of maximum amplitude.
The preceeding calculations express, of course, theoretical performance. In a real system using this technique there will always be some flutter noise present even when no signal is present (m= 0), primarily because of slight variations in the gain and phase responses of the two low-pass filters necessary for the demodulation of the two channels.
It follows from my expression for the frequency outputs of the data and reference channels that to perform perfect compensation (i.e., remove all flutter-generated noise for any modulation value), a theoretically perfect demodulator would have to perform division of the data channel playback frequency by the reference channel playback frequency, i.e., ##EQU6## which results in a constant (1) and the desired data signal (m). Subtracting the constant leaves only the data signal with all amplitude noise caused by the flutter completely eliminated.
One possible system to accomplish this involves an analog divider circuit. However, highly accurate and stable division is a relatively difficult function to perform with analog circuitry. Devices which are currently available to perform such functions are not only expensive, but fall short of the ideal device in their operation, being prone to such phenomena as temperature instability, "dc" drift, non-linearity, limited frequency response, and internally generated noise.
Another possible system attempts flutter removal utilizing computer-based digital techniques. The system measures the frequencies of the reference and data channels and stores this information in the computer, where the mathematical process of division is performed upon the frequencies, resulting in the "true" value for f.sub.D which can then be mathematically demodulated to yield the information transmitted. Besides requiring a computer and associated peripheral equipment, the overall result falls short of the theoretical values, due primarily to the fact that:
a. the measurement of frequency requires sampling over a time interval. The more accurate the desired measurement, the longer must be the time over which the sample is taken. Because the frequencies are usually changing during the sampling period, the figures which are later operated upon may not be of sufficient accuracy, and
b. overall accuracy is limited by the finite word length used in the calculations.
Another possibility is a system where the input data signal is digitalized via an analog-to-digital converter, the resulting samples being recorded in digital form. The playback process then consists of passing each sample through a digital-to-analog converter to reconstruct the original data signal. The only effect of flutter in such a system is inaccuracy in the time base in the reproduced data, i.e., no amplitude noise is added to the output signal by the flutter. The system is limited in accuracy only by the number of bits used in the digitizing process. The sampling rate must be at least twice the frequency of the highest data frequency, and requires a fairly sophisticated digital recorder, as well as the required analog-to-digital and digital-to-analog converters. Such a system would be inherently quite expensive and would very likely require higher bandwidth capabilities in the recording process than would a comparable FM system. Although such a system would be many times more expensive than a similar FM system, its improved performance over currently existing FM systems would justify the expense in many situations requiring a low-noise, high-performance recorder. These and other difficulties have been obviated in a novel manner by the present invention.
It is, therefore, an outstanding object of the invention to provide a noise-reduction system for removing flutter noise from a tape-recorded frequency-modulated data stream.
Another object of this invention is the provision of a noise-reduction system for allowing reproduction of frequency-modulated data read from an inexpensive audio cassette tape recorder with peak-to-peak signal-to-noise ratio of better than 60 db over a flat bandwidth of from 0 to 100 Hz.
A further object of the present invention is the provision of a noise-reduction system which is inexpensive to manufacture, which is compact, and which is capable of a long life of useful service with a minimum of maintenance.
With these and other objects in view, as will be apparent to those skilled in the art, the invention resides in the combination of parts set forth in the specification and covered by the claims appended hereto.